Mixed Topic Worksheet Grades 6/7: Day 019
- 1
Question 1. The volume of a cone is 324π cm³.
The height of the cone is 12 cm.
Work out the slant height of the cone.Volume of Cones▶ Show worked answerHide worked answer
- M1: 1/3 × π × r² × 12 = 324π
- M1: r² = 81 so r = 9
- M1: l² = 9² + 12²
- A1: 15
Answer: 15[4 marks] - 2
Question 2. A box plot shows the marks of 80 students. The lower quartile is 41 and the upper quartile is 63. How many students scored between 41 and 63?
Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- M1: half of the students lie between the quartiles
- A1: 40
Answer: 40[2 marks] - 3
Question 3. A square has an area of 20 cm².
Is the perimeter of the square rational or irrational? Show your working.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: side = √20 = 2√5
- M1: perimeter = 4√20 = 8√5
- A1: irrational, because 8√5 cannot be written as a fraction of two integers
Answer: Irrational. Side = √20 = 2√5, perimeter = 8√5 cm.[3 marks] - 4
Question 4. Here is the graph of y = x + 1
Shade the region that satisfies y ≤ x + 1Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: tests a point, for example (0, 0) gives 0 ≤ 1 which is true
- A1: shades the region below the line, which contains (0, 0)
Answer: The region below the line is shaded (the line is solid).[2 marks] - 5
Question 5. Here are the first five terms of a quadratic sequence.
3 qquad 8 qquad 15 qquad 24 qquad 35 qquad ldots
Find an expression, in terms of n, for the nth term of this sequence.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: differences 5, 7, 9, 11 so the second difference is 2, giving n² (1, 4, 9, 16, 25)
- M1: the remainders 2, 4, 6, 8, 10 are 2n
- A1: n² + 2n
Answer: n² + 2n[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 019
- 1
Question 1. The volume of a cone is 324π cm³.
[4 marks]
The height of the cone is 12 cm.
Work out the slant height of the cone.Volume of Cones▶ Show worked answerHide worked answer
- M1: 1/3 × π × r² × 12 = 324π
- M1: r² = 81 so r = 9
- M1: l² = 9² + 12²
- A1: 15
Answer: 15 - 2
Question 2. A box plot shows the marks of 80 students. The lower quartile is 41 and the upper quartile is 63. How many students scored between 41 and 63?
[2 marks]Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- M1: half of the students lie between the quartiles
- A1: 40
Answer: 40 - 3
Question 3. A square has an area of 20 cm².
[3 marks]
Is the perimeter of the square rational or irrational? Show your working.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: side = √20 = 2√5
- M1: perimeter = 4√20 = 8√5
- A1: irrational, because 8√5 cannot be written as a fraction of two integers
Answer: Irrational. Side = √20 = 2√5, perimeter = 8√5 cm. - 4
Question 4. Here is the graph of y = x + 1
[2 marks]
Shade the region that satisfies y ≤ x + 1Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: tests a point, for example (0, 0) gives 0 ≤ 1 which is true
- A1: shades the region below the line, which contains (0, 0)
Answer: The region below the line is shaded (the line is solid). - 5
Question 5. Here are the first five terms of a quadratic sequence.
[3 marks]
3 qquad 8 qquad 15 qquad 24 qquad 35 qquad ldots
Find an expression, in terms of n, for the nth term of this sequence.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: differences 5, 7, 9, 11 so the second difference is 2, giving n² (1, 4, 9, 16, 25)
- M1: the remainders 2, 4, 6, 8, 10 are 2n
- A1: n² + 2n
Answer: n² + 2n
Mixed Topic Worksheet Grades 6/7: Day 019
- 1
Question 1. The volume of a cone is 324π cm³.
The height of the cone is 12 cm.
Work out the slant height of the cone.Volume of Cones▶ Show worked answerHide worked answer
- M1: 1/3 × π × r² × 12 = 324π
- M1: r² = 81 so r = 9
- M1: l² = 9² + 12²
- A1: 15
Answer: 15[4 marks] - 2
Question 2. A box plot shows the marks of 80 students. The lower quartile is 41 and the upper quartile is 63. How many students scored between 41 and 63?
Comparing Data Using Box Plots▶ Show worked answerHide worked answer
- M1: half of the students lie between the quartiles
- A1: 40
Answer: 40[2 marks] - 3
Question 3. A square has an area of 20 cm².
Is the perimeter of the square rational or irrational? Show your working.Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: side = √20 = 2√5
- M1: perimeter = 4√20 = 8√5
- A1: irrational, because 8√5 cannot be written as a fraction of two integers
Answer: Irrational. Side = √20 = 2√5, perimeter = 8√5 cm.[3 marks] - 4
Question 4. Here is the graph of y = x + 1
Shade the region that satisfies y ≤ x + 1Sketching Linear Inequalities▶ Show worked answerHide worked answer
- M1: tests a point, for example (0, 0) gives 0 ≤ 1 which is true
- A1: shades the region below the line, which contains (0, 0)
Answer: The region below the line is shaded (the line is solid).[2 marks] - 5
Question 5. Here are the first five terms of a quadratic sequence.
3 qquad 8 qquad 15 qquad 24 qquad 35 qquad ldots
Find an expression, in terms of n, for the nth term of this sequence.nth Term of Quadratic Sequences▶ Show worked answerHide worked answer
- M1: differences 5, 7, 9, 11 so the second difference is 2, giving n² (1, 4, 9, 16, 25)
- M1: the remainders 2, 4, 6, 8, 10 are 2n
- A1: n² + 2n
Answer: n² + 2n[3 marks]